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Beliebt Rechnen >

derivative of xln(x^2+1)

Lösung

\frac{d}{d x} (x ln (x^{2} + 1))

Lösung

ln (x^{2} + 1) + \frac{2 x ^{2}}{x ^{2} + 1}

Schritte zur Lösung

\frac{d}{d x} (x ln (x^{2} + 1))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = ln (x^{2} + 1)

= \frac{d x}{d x} ln (x^{2} + 1) + \frac{d}{d x} (ln (x^{2} + 1)) x

\frac{d x}{d x} = 1

\frac{d}{d x} (ln (x^{2} + 1)) = \frac{2 x}{x ^{2} + 1}

= 1 \cdot ln (x^{2} + 1) + \frac{2 x}{x ^{2} + 1} x

Vereinfache

1 \cdot ln (x^{2} + 1) + \frac{2 x}{x ^{2} + 1} x : ln (x^{2} + 1) + \frac{2 x ^{2}}{x ^{2} + 1}

= ln (x^{2} + 1) + \frac{2 x ^{2}}{x ^{2} + 1}

Graph

Beliebte Beispiele

integral of (e^x)/((1+e^x))

integral of (3+x)

integral of p(p+2)^6

derivative of 1/(x^2-3/(x^4))

fläche y=x^4,y=x